Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12522 |
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 101 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(70,72,81,95,75,84,85,97,73,82,96,101,86,98,74,83)(71,77,87,94,79,91,90,92,76,89,100,99,88,93,78,80);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,63,67,58,65,57,64)(55,59,66,69,61,68,60,62)(71,76)(77,89)(78,90)(79,88)(80,92)(87,100)(91,93)(94,99);(54,55,58,61)(56,62,65,69)(57,66,63,60)(59,67,68,64)(70,71)(72,80)(73,76)(74,87)(75,88)(77,83)(78,81)(79,86)(82,92)(84,99)(85,100)(89,97)(90,96)(91,101)(93,95)(94,98)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=eg,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^c=i^521058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84306);